Details

sample129.0ms

Algorithm

intervals

Results

66.0ms	158×	body	1280	valid
28.0ms	111×	body	640	valid
9.0ms	58×	body	320	valid
8.0ms	167×	body	80	valid
3.0ms	31×	body	160	valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	7
1	40	7
2	92	7
3	163	7
4	405	7
5	865	7
6	1189	7
7	2771	7
8	5001	7

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 44.8b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))
6.5b	(- (exp (- im)) (exp im))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

27×	`prod-diff`
26×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-r`
4×	`add-log-exp`
3×	`sub-neg` `fma-neg` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `associate-l` `*-commutative`

Counts

2 → 74

Calls

2 calls:

11.0ms	(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))
7.0ms	(- (exp (- im)) (exp im))

series113.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))
38.0ms	(- (exp (- im)) (exp im))

simplify47.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	371	1102
1	1544	774
2	5001	722

prune157.0ms

Filtered

80 candidates to 43 candidates (53.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	2	81

Merged error: 0.1b

Counts

81 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/60 (pow im 5) (* 2 im))
0.0b	(- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))
0.1b	(* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
0.1b	(* 1/3 (pow im 3))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

54×	`prod-diff`
48×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
37×	`add-cube-cbrt`
20×	`distribute-rgt-in` `distribute-lft-in`
17×	`associate-r`
14×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
9×	`pow1`
8×	`add-log-exp`
6×	`fma-neg` `prod-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `cube-prod` `associate-l` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `pow-prod-down`
2×	`flip3--` `diff-log` `associate-r/` `-commutative` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`associate--l-` `neg-sub0` `cube-mult` `pow-to-exp` `unpow3` `neg-log` `pow-exp` `associate--r+`

Counts

4 → 150

Calls

4 calls:

1.0ms	(fma 1/60 (pow im 5) (* 2 im))
6.0ms	(- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))
11.0ms	(* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
7.0ms	(* 1/3 (pow im 3))

series365.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(fma 1/60 (pow im 5) (* 2 im))
57.0ms	(- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))
164.0ms	(* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
34.0ms	(* 1/3 (pow im 3))

simplify92.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	586	2644
1	2556	1682
2	5002	1670

prune376.0ms

Filtered

162 candidates to 79 candidates (48.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	154	8	162
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	154	10	164

Merged error: 0.0b

Counts

164 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma 1/60 (pow im 5) (* 2 im))) (cbrt (fma 1/60 (pow im 5) (* 2 im))))
0.7b	(cbrt (fma 1/60 (pow im 5) (* 2 im)))
0.7b	(cbrt (fma 1/60 (pow im 5) (* 2 im)))
0.7b	(cbrt (fma 1/60 (pow im 5) (* 2 im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt (fma 1/60 (pow im 5) (* 2 im))) (cbrt (fma 1/60 (pow im 5) (* 2 im))))
1.0ms	(cbrt (fma 1/60 (pow im 5) (* 2 im)))
1.0ms	(cbrt (fma 1/60 (pow im 5) (* 2 im)))
1.0ms	(cbrt (fma 1/60 (pow im 5) (* 2 im)))

series2.3s

Counts

4 → 12

Calls

4 calls:

580.0ms	(* (cbrt (fma 1/60 (pow im 5) (* 2 im))) (cbrt (fma 1/60 (pow im 5) (* 2 im))))
559.0ms	(cbrt (fma 1/60 (pow im 5) (* 2 im)))
563.0ms	(cbrt (fma 1/60 (pow im 5) (* 2 im)))
548.0ms	(cbrt (fma 1/60 (pow im 5) (* 2 im)))

simplify108.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	293	1041
1	911	965
2	3966	833
3	5001	800

prune426.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	92	11	103

Merged error: 0.0b

Counts

103 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))) (cbrt (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))
0.7b	(cbrt (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
0.7b	(cbrt (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
0.7b	(cbrt (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
37×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

14.0ms	(* (cbrt (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))) (cbrt (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))
5.0ms	(cbrt (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
5.0ms	(cbrt (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
5.0ms	(cbrt (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))

series715.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(* (cbrt (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))) (cbrt (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))
172.0ms	(cbrt (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
171.0ms	(cbrt (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
169.0ms	(cbrt (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))

simplify67.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	418	2415
1	1532	2282
2	5001	2124

prune523.0ms

Filtered

121 candidates to 89 candidates (73.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	120	12	132

Merged error: 0.0b

Counts

132 → 12

regimes266.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	10
1	28	10
2	28	10

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.3s	4704×	body	1280	valid
935.0ms	3829×	body	640	valid
295.0ms	1841×	body	320	valid
220.0ms	4484×	body	80	valid
101.0ms	974×	body	160	valid